Problem $2$: Spam Email Classification

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline & $\backslash$begin$\{$tabular$\}\{$l$\}$

Sender $\backslash \backslash$

Domain $\backslash \backslash$

$($Nominal$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Email Length $\backslash \backslash$

$($Continuous$)$

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Attachment $\backslash \backslash$

$($Nominal$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Spam Link $\backslash \backslash$

Count $\backslash \backslash$

$($Discrete$)$

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Urgency $\backslash \backslash$

Level $\backslash \backslash$

$($Ordinal$)$

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Is $\backslash \backslash$

Sampam

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$\backslash$hline $1$ & example.com & $1323$ & No & $0$ & Low & No $\backslash \backslash$

$\backslash$hline $2$ & spammer.net & $542$ & Yes & $3$ & High & Yes $\backslash \backslash$

$\backslash$hline $3$ & legitimate.org & $981$ & No & $1$ & Medium & No $\backslash \backslash$

$\backslash$hline $4$ & example.com & $698$ & Yes & $5$ & High & Yes $\backslash \backslash$

$\backslash$hline $5$ & legitimate.org & $1234$ & No & $0$ & Low & No $\backslash \backslash$

$\backslash$hline $6$ & spammer.net & $322$ & No & $1$ & Medium & Yes $\backslash \backslash$

$\backslash$hline $7$ & example.com & $657$ & Yes & $4$ & Medium & No $\backslash \backslash$

$\backslash$hline $8$ & spammer.net & $987$ & No & $0$ & High & Yes $\backslash \backslash$

$\backslash$hline $9$ & legitimate.org & $445$ & Yes & $6$ & High & Yes $\backslash \backslash$

$\backslash$hline $10$ & legitimate.org & $1298$ & & & Now $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

You are tasked with classifying emails as spam or not spam using Naive Bayes classification. You need to estimate the conditional probabilities for different attributes and the class variable $"$Is Spam."

Exercises:

$1.$ Calculate Prior Probabilities: Calculate the prior probabilities of an email being spam or not spam based on the provided dataset.

$2.$ Conditional Probabilities for Nominal Attributes: Calculate the conditional probabilities of an email being spam or not spam for different sender domains $($Nominal attribute$).$

$3.$ Conditional Probabilities for Continuous Attributes: Calculate the conditional probabilities of an email being spam or not spam based on the email length $($Continuous attribute$).$ You can assume a Gaussian distribution.

$4.$ Conditional Probabilities for Nominal Attributes with Multiple Categories: Calculate the conditional probabilities of an email being spam or not spam based on whether it has an attachment $($Nominal attribute$).$

$5.$ Conditional Probabilities for Discrete Attributes: Calculate the conditional probabilities of an email being spam or not spam based on the number of spam links $($Discrete attribute$).$

$6.$ Conditional Probabilities for Ordinal Attributes: Calculate the conditional probabilities of an email being spam or not spam based on the urgency level $($Ordinal attribute$).$

$7.$ Spam Classification: Given a new email with the following attributes, use Naive Bayes to classify it as spam or not spam:

Sender Domain: "spammy.biz"

Email Length: $765$

Attachment: Yes

Spam Link Count: $2$

Urgency Level: Medium

These exercises will help you practice estimating probabilities for a Naive Bayes classification problem with different types of attributes.